Question

word problem!

The largest Ferris Wheel in the world is the London Eye in England. The height (in metres) of a rider on the London Eye after t minutes can be described by the function h(t) = 67sin[12(t + 0.0223)] + 70.

What is the diameter of this Ferris wheel?
Where is the rider at t = 0? Explain the significance of this value.
How high off the ground is the rider at the top of the wheel?
At what time(s) will the rider be at the bottom of the Ferris wheel?
How long does it take for the Ferris wheel to go through one rotation?

Answer 1

Always remember the max value for Sin(x) or Cos(x) is 1. So the highest the London Eye rider can get to is (67 x 1) + 70 = 137 m. The lowest value is Sin(x) = -1 so the lowest height is +70 - (67) = 3m. These give 137 - 3 = diameter = 134m.

To get the value of the lowest height, you need Sin(x) which is Sin(12(t+0.0223)) to be zero. This is at t= -0.0223 minutes and repeats every 12 minutes (the Period of the rotation).
I took my kids on it, next time I'll have to take this question with me.

Answer 2

Sorry, I posted this by mistake. before correcting the above.
The times the rider is at the bottom is when Sin(x) = -1 and this will be when theta (the equation inside Sin() is equivalent to \[(3/2)\pi\]
At first I read theta as (12(t)+0.0223), if this is wrong and it is 12(t + 0.0223) Then you need to convert this into fractions of 2 Pi which tells you how far around the cycle a reference point (cabin) is.